def testGenerateSSIPtriangulation(points):
"""
input: vertices and SSIP points belonging to a single element
generate triangle representation of the points
output: an array contaning the points, and element quadrature weights for the points
test with input
import numpy
from proteus import TriangleTools
points = numpy.array([[0.0,0.0,0.0],[0.5,0.4,0.],[1.0,0.0,0.0],[0.2,0.3,0.0],[0.0,1.0,0.0]])
dV,x = TriangleTools.testGenerateSSIPtriangulation(points)
"""
#mwf debug
#import pdb
#pdb.set_trace()
#default representation for holding input points
tri0 = triangleWrappers.new()
triangleWrappers.setPoints(tri0, points[:, :2])
flags = "z" #"qz" #just use simple quality mesh generation, number from zero
#default representation for holding output points
tri1 = triangleWrappers.new()
triangleWrappers.applyTriangulateNoVoronoi(flags, tri0, tri1)
#doing all the necessary generation of quadrature points
#and weights internally don't need deep copy
nodeArray2d = triangleWrappers.getPoints(tri1)
elementNodesArray = triangleWrappers.getTriangles(tri1)
import Quadrature, cfemIntegrals
#try Gauss quadrature different orders
#subElementQuadrature = Quadrature.GaussTriangle()
#subElementQuadrature.setOrder(2) #order(1)
#What about vertex quadrature
subElementQuadrature = Quadrature.LobattoTriangle()
subElementQuadrature.setOrder(3)
nSubQuadraturePoints = len(subElementQuadrature.weights)
nElements = elementNodesArray.shape[0]
nQuadraturePoints = nElements * nSubQuadraturePoints
nSpace = 2
nDOF_element = 3
weights_ref = numpy.array(subElementQuadrature.weights)
points_ref = numpy.array(subElementQuadrature.points)
#loop through elements, compute area, map reference points to physical space,
#and compute physical space weights
#to be consistent need to have nodes be 3d
nodeArray = numpy.zeros((nodeArray2d.shape[0], 3), 'd')
nodeArray[:, 0:2] = nodeArray2d
#need to store psi and grad_psi to avoid recalculating across a lot of elements?
#shape functions are 1-x-y, x, y
psi = numpy.zeros((nSubQuadraturePoints, nDOF_element), 'd')
psi[:, 0] = 1.0 - points_ref[:, 0] - points_ref[:, 1]
psi[:, 1] = points_ref[:, 0]
psi[:, 2] = points_ref[:, 1]
#for k in range(nSubQuadraturePoints):
# psi[k,0] = 1.0-subElementQuadrature.points[k][0]-subElementQuadrature.points[k][1]
# psi[k,1] = subElementQuadrature.points[k][0]
# psi[k,2] = subElementQuadrature.points[k][1]
grad_psi = numpy.zeros((nSubQuadraturePoints, nDOF_element, nSpace), 'd')
#shape functions are 1-x-y, x, y
grad_psi[:, 0, 0].fill(-1.)
grad_psi[:, 0, 1].fill(-1.)
grad_psi[:, 1, 0].fill(1.0)
grad_psi[:, 2, 1].fill(1.0)
#waste space to reuse code
jacobianArray = numpy.zeros(
(nElements, nSubQuadraturePoints, nSpace, nSpace), 'd')
jacobianDetArray = numpy.zeros((nElements, nSubQuadraturePoints), 'd')
jacobianInvArray = numpy.zeros(
(nElements, nSubQuadraturePoints, nSpace, nSpace), 'd')
cfemIntegrals.parametricMaps_getJacobianValues(grad_psi, elementNodesArray,
nodeArray, jacobianArray,
jacobianDetArray,
jacobianInvArray)
jacobianDetArrayAbs = numpy.absolute(jacobianDetArray)
#weights and points shaped like nSubElements x nQuadraturePointsSubElement
q_sub_dV = numpy.zeros((nElements, nSubQuadraturePoints), 'd')
q_sub_x = numpy.zeros((nElements, nSubQuadraturePoints, 3), 'd')
cfemIntegrals.calculateIntegrationWeights(jacobianDetArrayAbs, weights_ref,
q_sub_dV)
cfemIntegrals.parametricMaps_getValues(psi, elementNodesArray, nodeArray,
q_sub_x)
#clean up
del tri0
del tri1
#exit
return q_sub_dV, q_sub_x
def testGenerateSSIPtriangulation(points):
"""
input: vertices and SSIP points belonging to a single element
generate triangle representation of the points
output: an array contaning the points, and element quadrature weights for the points
test with input
import numpy
from proteus import TriangleTools
points = numpy.array([[0.0,0.0,0.0],[0.5,0.4,0.],[1.0,0.0,0.0],[0.2,0.3,0.0],[0.0,1.0,0.0]])
dV,x = TriangleTools.testGenerateSSIPtriangulation(points)
"""
#mwf debug
#import pdb
#pdb.set_trace()
#default representation for holding input points
tri0 = triangleWrappers.new()
triangleWrappers.setPoints(tri0,points[:,:2])
flags = "z"#"qz" #just use simple quality mesh generation, number from zero
#default representation for holding output points
tri1 = triangleWrappers.new()
triangleWrappers.applyTriangulateNoVoronoi(flags,tri0,tri1)
#doing all the necessary generation of quadrature points
#and weights internally don't need deep copy
nodeArray2d = triangleWrappers.getPoints(tri1)
elementNodesArray = triangleWrappers.getTriangles(tri1)
import Quadrature,cfemIntegrals
#try Gauss quadrature different orders
#subElementQuadrature = Quadrature.GaussTriangle()
#subElementQuadrature.setOrder(2) #order(1)
#What about vertex quadrature
subElementQuadrature = Quadrature.LobattoTriangle()
subElementQuadrature.setOrder(3)
nSubQuadraturePoints = len(subElementQuadrature.weights)
nElements = elementNodesArray.shape[0]
nQuadraturePoints = nElements*nSubQuadraturePoints
nSpace = 2
nDOF_element = 3
weights_ref = numpy.array(subElementQuadrature.weights)
points_ref = numpy.array(subElementQuadrature.points)
#loop through elements, compute area, map reference points to physical space,
#and compute physical space weights
#to be consistent need to have nodes be 3d
nodeArray = numpy.zeros((nodeArray2d.shape[0],3),'d')
nodeArray[:,0:2] = nodeArray2d
#need to store psi and grad_psi to avoid recalculating across a lot of elements?
#shape functions are 1-x-y, x, y
psi = numpy.zeros((nSubQuadraturePoints,nDOF_element),'d')
psi[:,0] = 1.0-points_ref[:,0]-points_ref[:,1]
psi[:,1] = points_ref[:,0]
psi[:,2] = points_ref[:,1]
#for k in range(nSubQuadraturePoints):
# psi[k,0] = 1.0-subElementQuadrature.points[k][0]-subElementQuadrature.points[k][1]
# psi[k,1] = subElementQuadrature.points[k][0]
# psi[k,2] = subElementQuadrature.points[k][1]
grad_psi = numpy.zeros((nSubQuadraturePoints,nDOF_element,nSpace),'d')
#shape functions are 1-x-y, x, y
grad_psi[:,0,0].fill(-1.); grad_psi[:,0,1].fill(-1.)
grad_psi[:,1,0].fill(1.0);
grad_psi[:,2,1].fill(1.0)
#waste space to reuse code
jacobianArray = numpy.zeros((nElements,nSubQuadraturePoints,nSpace,nSpace),'d')
jacobianDetArray = numpy.zeros((nElements,nSubQuadraturePoints),'d')
jacobianInvArray = numpy.zeros((nElements,nSubQuadraturePoints,nSpace,nSpace),'d')
cfemIntegrals.parametricMaps_getJacobianValues(grad_psi,
elementNodesArray,
nodeArray,
jacobianArray,
jacobianDetArray,
jacobianInvArray)
jacobianDetArrayAbs = numpy.absolute(jacobianDetArray)
#weights and points shaped like nSubElements x nQuadraturePointsSubElement
q_sub_dV = numpy.zeros((nElements,nSubQuadraturePoints),'d')
q_sub_x = numpy.zeros((nElements,nSubQuadraturePoints,3),'d')
cfemIntegrals.calculateIntegrationWeights(jacobianDetArrayAbs,
weights_ref,
q_sub_dV)
cfemIntegrals.parametricMaps_getValues(psi,
elementNodesArray,
nodeArray,
q_sub_x)
#clean up
del tri0
del tri1
#exit
return q_sub_dV,q_sub_x